S matrix of collective field theory

By applying the Lehmann-Symanzik-Zimmermann (LSZ) reduction formalism, we study the S matrix of collective field theory in which fermi energy is larger than the height of potential. We consider the spatially symmetric and antisymmetric boundary conditions. The difference is that S matrices are proportional to momenta of external particles in antisymmetric boundary condition, while they are proportional to energies in symmetric boundary condition. To the order of $g_{st}^2$, we find simple formulas for the S matrix of general potential. As an application, we calculate the S matrix of a case which has been conjectured to describe a "naked singularity".Comment: 19 page, LaTe

Quantum and Classical Aspects of Deformed c=1c=1 Strings.

The quantum and classical aspects of a deformed $c=1$ matrix model proposed by Jevicki and Yoneya are studied. String equations are formulated in the framework of Toda lattice hierarchy. The Whittaker functions now play the role of generalized Airy functions in $c<1$ strings. This matrix model has two distinct parameters. Identification of the string coupling constant is thereby not unique, and leads to several different perturbative interpretations of this model as a string theory. Two such possible interpretations are examined. In both cases, the classical limit of the string equations, which turns out to give a formal solution of Polchinski's scattering equations, shows that the classical scattering amplitudes of massless tachyons are insensitive to deformations of the parameters in the matrix model.Comment: 52 pages, Latex

Systematic 1/N1/N corrections for bosonic and fermionic vector models without auxiliary fields

In this paper, colorless bilocal fields are employed to study the large $N$ limit of both fermionic and bosonic vector models. The Jacobian associated with the change of variables from the original fields to the bilocals is computed exactly, thereby providing an exact effective action. This effective action is shown to reproduce the familiar perturbative expansion for the two and four point functions. In particular, in the case of fermionic vector models, the effective action correctly accounts for the Fermi statistics. The theory is also studied non-perturbatively. The stationary points of the effective action are shown to provide the usual large $N$ gap equations. The homogeneous equation associated with the quadratic (in the bilocals) action is simply the two particle Bethe Salpeter equation. Finally, the leading correction in $1\over N$ is shown to be in agreement with the exact $S$ matrix of the model.Comment: 24 pages, uses REVTEX macros. Replaced with final version to appear in Phys. Rev.

Perturbation Theory in Two Dimensional Open String Field Theory

In this paper we develop the covariant string field theory approach to open 2d strings. Upon constructing the vertices, we apply the formalism to calculate the lowest order contributions to the 4- and 5- point tachyon--tachyon tree amplitudes. Our results are shown to match the `bulk' amplitude calculations of Bershadsky and Kutasov. In the present approach the pole structure of the amplitudes becomes manifest and their origin as coming from the higher string modes transparent.Comment: 26 page

One-dimensional classical adjoint SU(2) Coulomb Gas

The equation of state of a one-dimensional classical nonrelativistic Coulomb gas of particles in the adjoint representation of SU(2) is given. The problem is solved both with and without sources in the fundamental representation at either end of the system. The gas exhibits confining properties at low densities and temperatures and deconfinement in the limit of high densities and temperatures. However, there is no phase transition to a regime where the string tension vanishes identically; true deconfinement only happens for infinite densities and temperatures. In the low density, low temperature limit, a new type of collective behavior is observed.Comment: 6 pages, 1 postscript figur

Towards Solving QCD in Light-Cone Quantization -- On the Spectrum of the Transverse Zero Modes for SU(2)

The formalism for a non-abelian pure gauge theory in (2+1) dimensions has recently been derived within Discretized Light-Cone Quantization, restricting to the lowest {\it transverse} momentum gluons. It is argued why this model can be a paradigm for full QCD. The physical vacuum becomes non-trivial even in light-cone quantization. The approach is brought here to tractable form by suppressing by hand both the dynamical gauge and the constraint zero mode, and by performing a Tamm-Dancoff type Fock-space truncation. Within that model the Hamiltonian is diagonalized numerically, yielding mass spectra and wavefunctions of the glue-ball states. We find that only color singlets have a stable and discrete bound state spectrum. The connection with confinement is discussed. The structure function of the gluons has a shape like $[{x(1-x)}] ^{1\over 3}$. The existence of the continuum limit is verified by deriving a coupled set of integral equations.Comment: 1 Latex file & 9 Postscript files; tarred, compressed and uuencode

On the spectrum of QCD(1+1) with large numbers of flavours N_F and colours N_C near N_F/N_C = 0

QCD(1+1) in the limit of a large number of flavours N_F and a large number of colours N_C is examined in the small N_F/N_C regime. Using perturbation theory in N_F/N_C, stringent results for the leading behaviour of the spectrum departing from N_F/N_C = 0 are obtained. These results provide benchmarks in the light of which previous truncated treatments of QCD(1+1) at large N_F and N_C are critically reconsidered.Comment: 6 revtex page